The Spectator's Fraser Nelson and Ian Hislop of Private Eye have become the first magazine editors to decline to join the new press regulator, 24 hours after it was unveiled by the prime minister before parliament.

Nelson said his political weekly, which is owned by Daily Telegraph proprietors the Barclay brothers, could not be part of a system that involved "state licensing of the media".

"Press regulation is too important an issue to be answered by some tawdry deal cooked up at two in the morning in Ed Miliband's office," he told BBC Radio 4's PM programme on Tuesday. "It's not something the Spectator feels like signing up to."

Nelson was referring to the agreement on a new regulatory regime negotiated between the three main parties in the early hours of Monday morning, with members of the Hacked Off group that campaigns on behalf of victims of press intrusion in attendance.

Hislop, the editor of Private Eye, which is not part of the existing discredited regulatory system overseen by the Press Complaints Commission, said he had no intention of joining the regulator enshrined in royal statute.

The Have I Got News For You broadcaster said he was "confused" about whether the system was statutory underpinning or not. "Everything about it makes me think: 'I didn't belong to the previous regulator, I don't want to belong to this one'," he told the PM programme.

Hislop said he had not been involved in political talks ahead of the cross-party deal, adding that it was difficult "as an independent voice" knowing what regulatory framework to sign up to.

"You cant really say this is a considered and thoughtful process when, in the middle of the night, bits are added to two different bills," he said. "This doesn't really look like thoughtful considered legislation that has been thought through."